tidal truncation and barotropic convergence in a channel ... · the east and west asymmetric tides...

Tidal truncation and barotropic convergence in a channelnetwork tidally driven from opposing entrances

J.C. Warnera,b,*, D. Schoellhamera, G. Schladowb

aU.S. Geological Survey, Sacramento, CA, USAbUniversity of California, Davis, CA, USA

Received 16 October 2001; received in revised form 4 March 2002; accepted 19 March 2002

Abstract

Residual circulation patterns in a channel network that is tidally driven from entrances on opposite sides are controlled by thetemporal phasing and spatial asymmetry of the two forcing tides. The Napa/Sonoma Marsh Complex in San Francisco Bay, CA, is

such a system. A sill on the west entrance to the system prevents a complete tidal range at spring tides that results in tidal truncationof water levels. Tidal truncation does not occur on the east side but asymmetries develop due to friction and off-channel wetlandstorage. The east and west asymmetric tides meet in the middle to produce a barotropic convergence zone that controls the transport

of water and sediment. During spring tides, tidally averaged water-surface elevations are higher on the truncated west side. Thiscreates tidally averaged fluxes of water and sediment to the east. During neap tides, the water levels are not truncated and the prop-agation speed of the tides controls residual circulation, creating a tidally averaged flux in the opposite direction.

� 2003 Elsevier Science B.V. All rights reserved.

Keywords: channel network; tidal truncation; residual circulation; barotropic convergence; San Francisco Bay

1. Introduction

Estuarial and coastal settings may consist of complexgeometric patterns that create channels subjected to ti-dal forcings from both ends. Circulation patterns ofwater and suspended sediment through these systemsare controlled by the magnitude and phasing of thebounding tidal forcings. Previous analytical investiga-tions on canals subjected to tidal forcings at both endshave concentrated on solutions to linearized governingequations. Einstein and Fuchs (1954) and Parsons(1918) used similar sets of equations to describe the cur-rents and water-level variations in the Cape Cod Canaland the proposed Panama Sea Level Canal, respectively.Dronkers (1964, p. 240) derived a more general expres-sion with dependence on the total flow with the solutionthen applicable to any channel shape. Wong (1990)

developed a linearized, frequency-dependent model toexamine spatial distributions of tidal and subtidalvariability along the length of the Chesapeake and Del-aware Canal. All of these investigations considered deepchannels with small ratios of tidal amplitude to meanwater depth ðg=h� 1Þ. Resulting water levels were func-tions of the phase and magnitude of the driving waterlevels at the ends of the canal and the velocities essen-tially were determined by a balance between frictionand the elevation head difference between the ends ofthe canal (Wilcox, 1958). The time of current reversalmay not coincide directly with the time of head reversal,owing to the need to overcome the momentum of thesystem.

In a more shallow system, Parker (1991) briefly dem-onstrated the effect of a dominant semidiurnal waterlevel, but a quarter-diurnal current variation due to alinear superposition of opposing (cancelling) predomi-nant M2 currents that allowed M4 terms to becomedominant and additive.

The shallow water tidal slough channels for thepresent study area (ratio of tidal displacement (g) to

* Corresponding author.

E-mail address: [email protected] (J.C. Warner).

Estuarine, Coastal and Shelf Science 56 (2003) 629–639

0272-7714/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0272-7714(02)00213-5

mean depth is in the order of 1) are shown in Fig. 1. Thetidal forcing is a shallow water gravity wave that origi-nates from the Pacific Ocean and enters San FranciscoBay through the Golden Gate, propagating throughCentral Bay to enter the study area from two directions:(1) northward across the broad shallow San Pablo Bayand into the west entrance at Sonoma Creek, and (2)eastward along the main shipping channel to CarquinezStrait and into the east entrance at the Napa River. Be-tween these two entrances, the study area consists of anetwork of interconnected tidal channels with depthsin the order of 2m (relative to mean lower low water(MLLW)) and a tidal range of 2m. The Napa Riverhas a depth of 9m MLLW near the mouth and de-creases to approximately 4m MLLW near the upperpart of the study area (Warner, Schladow, and Schoell-hamer, 1999).

The purpose of this paper is to describe the physicalprocesses that control the tidal and tidally averaged timescale circulation patterns in a shallow channel networkthat is tidally driven from opposing entrances. Thesephysical processes result in temporal and spatial asym-metry in the channel system.

2. Data collection

Equipments to measure water conductivity, tempera-ture and depth (CTD), and velocity magnitude and di-rection using acoustic Doppler profilers (ADP) orelectromagnetic current metres (EMCM) (Table 1) weredeployed at eight sites (Fig. 2): Pablo, Socr, SNS, Hude,Buchli, Pipe, MIC, and M5 from 2 September 1997 to 12March 1998. Additionally, water-level data are refer-enced from the long-term US Geological Survey(USGS) station, PSP. Measurements at all sites typicallywere recorded on a 10-min time step. Continuous datasets were not obtained from all the sites for all parame-ters due to instrument difficulties and biological fouling(Warner et al., 1999).

2.1. Tidal truncation effects

Tidal truncation occurs when the water level does notexperience a complete tidal range. This can occur on thelandward side of a sill where the water level only reducesto the level of the sill at low tide. On the seaward side ofthe sill, the water level can reduce to match the forcingocean tide. To explain this process and its effects inthe study area, harmonic analysis is first used to describethe propagation of the tide, then principal componentsanalysis (PCA) denotes the spatial extent of the trunca-tion influence, and, lastly, a momentum balance showsthe effects of tidal truncation.

2.1.1. Water-level harmonic analysisTo determine spatial development of tidal asymme-

tries and to quantify the propagation of the tide fromboth ends of the system, the measured water-level timeseries for all sites were first decomposed into their har-monic constants using a least-squares analysis computerprogram developed by Foreman (1978) and modified byGartner (1997) for a USGS standard data format. Thedata used for the analysis typically consisted of thecontinuous first 3 months of recoverable water-level re-cord from each site, during which time freshwater inflowwas constant and minimal. Freshwater inflows have

Fig. 1. General flood current directions in study area, San Francisco

Bay, CA.

Table 1

Heights of instruments above the bed

Vertical distance (m) from

the bed to the sensor

Site CTD Velocity

M5 1, 6 ADP—0.5mbins

MIC 1, 7 ADP—0.5mbins

Buchli, SNS, Hude, Pipe 0.3 EMCM—0.45m

Socr, Pablo 0.3 EMCM—0.45m

m: Metres; CTD: conductivity, temperature, depth; ADP: acoustic

Doppler profiler; EMCM: electromagnetic current metre.

630 J.C. Warner et al. / Estuarine, Coastal and Shelf Science 56 (2003) 629–639

been shown to alter the phase and amplitude of tidalconstituents (Parker, 1991) and therefore this periodof low flow was selected. All of the sites showed domi-nateastronomical constituentsofM2,K1, andO1,as typi-cally is observed in San Francisco Bay (Walters, Cheng,& Conomos, 1985). The principal harmonic constituentsresolved at each site are given in Table 2. Error analysison the residual signal (original series less the harmonic

components) revealed maximum errors in amplitudeand phase in the order of 1 cm and 6�, respectively.

The M2 constituent is the most dominant partial tide(based on its amplitude) and its phase can be used tocharacterize the propagation of the tide throughoutthe system. As one enters the slough system from eitherside the M2 arrival time becomes progressively later to-wards the middle. Fig. 3 shows the arrival time of thetide at each site based on the M2 constituent of waterlevel. An estimate of the propagation speed of the tideis c¼ ffiffiffi

gp

h and using average depths of 3m for the westside (Sonoma Creek) and 7m for the east side (NapaRiver) yield speeds of 5.5 and 8.5m s�1, respectively.The distance from Pablo to SNS is 6500m which givesa travel time of approximately 6500m/(5.5m s�1)¼20min. Fig. 3 shows the arrival of the M2 partial tide as17min, which is comparable. Travel times on the east sideare faster because of the greater depths and the 16,400mdistance is travelled by theM2 partial tide in 33min fromsiteM5 to Buchli. Fig. 3 also shows that the incoming tidearrives first at the west side in the order of 5min.

Because the largest astronomical tidal constituentsare the M2, O1, and K1, the resulting predominantshallow water tides will be the M4, MO3, and MK3,of which the last two components enhance diurnal in-equality (Aubrey & Speer, 1985). The M4 is responsiblefor creating temporal asymmetry such as a longer dura-tion to low tide. Increased amplitudes of these shallowwater constituents identify locations of increased tidalasymmetry. The magnitudes of these shallow waterconstituents (Fig. 4) are plotted spatially along the loopof sites PSP–Pablo–Socr–SNS–Hude–Buchli–MIC–M5(Fig. 2). Amplification of shallow water tides occursnear and on the landward side of site Pablo. How-ever, as one travels along the navigable path past Hudeand to the east side of the network, the magnitudes ofthe shallow water partial tides decrease. For example,the MO3 has a magnitude of 6.5 cm at site Pablo, but itdecreases to less than one-half of this (3 cm) at site PSP.The decrease suggests that some physical process nearsite Pablo is producing nonlinearities in the tide.

Table 2

Selected water-level tidal harmonic constituents

Diurnal Semidiurnal Compound Overtide

Site 23.93 h, K1 26.87 h, O1 12.42 h, M2 12.00 h, S2 8.39 h, MO3 8.18 h, MK3 6.21 h, M4

Pablo 32.1/132.0 19.5/127.2 64.3/22.4 13.6/27.1 6.4/87.9 5.6/70.3 4.3/329.8

Socr 32.2/140.7 18.5/134.6 66.1/34.5 13.3/44.1 6.7/93.3 4.7/68.1 3.4/329.9

SNS 32.1/138.9 18.3/132.6 66.4/30.81 13.4/41.0 6.8/88.1 4.6/63.4 3.4/325.6

Hude 31.8/144.3 18.2/135.7 71.2/39.8 14.7/51.2 5.6/113.5 2.5/93.7 1.2/286.6

Buchlia 32.2/140.8 – 69.1/40.9 – – – 2.4/255.8

MIC 25.1/124.0 20.0/123.2 65.4/27.1 16.5/22.0 3.5/107.0 1.7/110.6 1.1/268.1

M5 26.8/122.9 19.5/124.2 61.6/25.0 15.2/18.6 3.5/101.8 1.5/86.8 1.9/248.7

PSP 35.3/120.0 21.5/110.2 59.4/3.7 13.2/3.25 2.9/106.7 2.2/135.8 1.6/73.5

Constituent values shown as amplitude/degrees. Amplitude is given in centimetres and phase is given in degrees. – Implies unresolved

constituents.a Short time series due to instrument difficulties.

Fig. 2. Loop of sites PSP–Pablo–Socr–SNS–Hude–Buchli–MIC–

M5. Bathymetry of San Pablo Bay obtained from Jaffe, Smith, and

Zink (1998) (http://sfbay.wr.usgs.gov/access/sanpablobay/bathy/

bathy.html). , marsh; , tidal mudflat; , 6-foot contour mean

lower low water; , 30-foot contour mean lower low water;

, loop of sites; ., data collection site.

631J.C. Warner et al. / Estuarine, Coastal and Shelf Science 56 (2003) 629–639

A water-level prediction was performed using thesame harmonic constants (principal and nonlinear con-stituents) and for the same time period as for thewater-level analysis (Fig. 5). The predicted time seriesfor site M5 compares favourably with the original mea-sured time series, however, the predicted time series ofwater level for site Pablo does not fit well, especiallywhen depths slowly decrease to the lower low tides. Thisnonreproducibility of the tide from harmonic constantsis an indication of the occurrence of a nonlinear, non-harmonic physical process. This process has been

observed by Lincoln and Fitzgerald (1988) and is termedtidal truncation.

Tidal truncation occurs when an obstruction to theflow is present in the main channel, truncating the tidefor the low water levels. A low-lying tidal mudflat cutsacross the entrance to Sonoma Creek (Fig. 2) withdepths less than 0 ft below MLLW. This mudflat actsas a sill or an obstruction to the flow. On the landwardside of the sill, the tidal water-level fluctuations are trun-cated at the level of the sill, whereas on the seaward sideof the sill, the water level can descend to match the forc-ing tide. Site Pablo is located on the landward side of thesill and, therefore, will display the truncating effect.Thus, a full ebb from Sonoma Creek (past site Socr, Pa-blo, and the west side) will not be allowed to develop,and the start to the rising tide will also be delayed.

Tidal truncation effects are greatest during springtides when the tidal range is increased, as observed bycomparing the water-level time series from sites Pabloand M5. During spring tides (Fig. 6a), the increased ti-dal range allows the water level at site M5 (and in thebay) to decrease below the level of the sill. At thesetimes, an increased frictional effect and the sill elevationprevent the flow at site Pablo from ebbing completely.The slow decrease of water level observed at site Pablomost likely is due to a steady discharge from SonomaCreek and associated drainage from tidal wetlands inthe system. Therefore, the time to �low tide� will continueuntil the rising tide has had the opportunity to overtopthe sill elevation. The low tide occurs 1.5 h after low tideat site M5 for the lower low tide (Fig. 6a). This springtide had a slight diurnal inequality, and the higher lowtide has a 0.5-h lag behind the low tide on the east side.In either case, this delay will be shown to be critical forcirculation patterns in the network. During neap tides(Fig. 6b) the timing of low tide almost is in phase with,or occurs earlier at, site Pablo than at site M5. The dif-ference occurs because the elevation of the low tidesdoes not fall below the sill elevation in San Pablo Bay,and the ebb on the west side is not truncated.

2.1.2. Water-level principal components analysisTo determine the spatial extent of the truncation ef-

fect, PCA was performed on the water-level time series.PCA (Preisendorfer, 1988) is a numerical method thatrepresents n time series as n components (eigenvectors)that co-vary in time (Fig. 7). The relative contributionof each component is determined by the eigenvalues ofthe covariance matrix of the time series. For the analysisof the water-level time series, the first three principalcomponents contain 98% of the variability of the systemand explain 95, 2, and 1% of the variance, respectively.

Fig. 7 shows the spatial variation of each principalcomponent and their associated amplitude time series.PC1 is spatially homogenous and the amplitude timeseries corresponds to the astronomical tidal variability

Fig. 3. Arrival time of tide (based on phase of M2 constituent of water

level) relative to site Pablo vs. distance from site Pablo. Slopes provide

approximate propagation speed of the tide (c) and show a faster travel

time on the east side.

Fig. 4. Spatial variation of selected shallow water tidal harmonic

constituents from analysis of water level for loop PSP–Pablo–Socr–

SNS–Hude–Buchli–MIC–M5. Maximum tidal nonlinearities occur

near site Pablo (- - -, MO3; ��, MK3; —�—�—, M4).


Fig. 5. Comparison of measured and harmonically predicted time series of water level from sites (a) Pablo and (b) M5. The reconstruction of the time

series for site Pablo cannot reproduce the long lags at low water (—, field data; - - - -, reconstructed).

Fig. 6. Influence of tidal sill truncation. (a) Spring tides showing increased tidal asymmetry at site Pablo, especially at lower low water, (b) neap tides

showing negligible shallow water truncation. Note: M5 water level approximated, Pablo water level related to survey datum of WGS-84 (—, M5;

———, Pablo).

of the system, representing the semidiurnal and spring/neap tidal variability. PC2 varies spatially from negativevalues at the two boundary stations to a positive maxi-mum value near the centre of the loop. This representsthe lag of the tide as it propagates through the networkto converge near the centre (similar to Fig. 3). The am-plitude time-series plot for PC2 varies semidiurnally andwith the spring/neap tidal cycle to represent varyingpropagation speeds, in relation to changes in meandepth. PC3 has negative values at the western sites, pos-itive values at the east sites and approximately a zerovalue near the middle. The amplitude time series forPC3 compliments the spatial variation of the shallowwater tides (Fig. 4). The amplitude time series for PC3temporally varies the same as the difference in water-surface elevation across the network, due to the tidaltruncation effect. PC3 has increased magnitudes duringspring tides when the truncation effect is dominant, dueto increased tidal ranges. PC3 is important, as it demar-cates the spatial extent of the truncation effect and delin-eates the slough network into three separate systems.The west side is defined by the positive values of PC3to show the truncation effect at sites Pablo, Socr, andSNS. The component shows a lack of truncation effecton the east side defined by stations Buchli, MIC, andM5. Site Hude is located at a convergence from both

sides. With these spatial variations of PC3, the studyarea is demarcated into three regions: west side, baro-tropic convergence, and east side (Fig. 8).

2.1.3. VelocityThe truncating sill affects the velocities by creating

longer durations of slack tide at lower low water andrapid increases in velocity when the sill is overtopped.During spring tides, as the water-surface elevation re-duces to the level of the sill, the influence of frictionand the tidal truncating effect will reduce the magnitudesof the velocities. As seen near day 258.25 (Fig. 9b) thespring tidal water level has decreased to an elevationof 0m MLLW at sites Pablo and SNS. At this time,the velocities have slowed to a minimal magnitude ofapproximately 5–10 cm s�1 for a duration of nearly 1.5 hat sites Pablo and SNS. At this time, tidal current atSonomaCreek (site Socr) was ebbing slightly (not shown)from upstream wetland drainage. Current at site Pablois limited by the sill, so the ebb must flow east past siteSNS. The velocity at site SNS shows an eastward (pos-itive) direction with a magnitude of approximately10 cm s�1 towards site Hude.

The long duration of slack is ended when the risingwater level in the bay overtops the sill (day 258.3),

Fig. 7. Principal components and associated amplitude time series for water-level analysis. Eigenvectors show the magnitude of each component at

each site. The time series show how each component varies in time. PC3 is used to demarcate the study area into three regions.


correlating with the sudden turn of velocities to theflood direction for sites Pablo and SNS. The velocitiesincrease from slack to near 70 cm s�1 in 80min, whichis in the order of qu=qt � 1� 10�4 m s2, suggesting thattemporal acceleration may be important. A momentumbalance on the well-mixed longitudinal flow in theslough channels can be performed with the one-dimen-sional shallow water momentum and continuity equa-tions described by Ippen (1966). Using the velocity andwater-level field data from sites Pablo and Socr, the dis-tance of 6100m, and a Manning n value of 0.015, themomentum balance (in units of m s�2) scales as

qhuiqt

þ huiqhuiqx

¼ �gqgqx

� gn2huijhuijðhþ gÞ4=3

ð1Þ

10�4 10�5 10�4 10�4

temporal convective barotropic friction

acceleration acceleration gradient

where huðx; tÞi is the cross sectionally averaged velocity, tthe time, x the longitudinal direction, gðx; tÞ the water-surface displacement measured positive upwards fromthe mean water level, and g is the acceleration due togravity. This scaling shows that the temporal accelera-tion term is in the same order of magnitude as the bar-otropic gradient and the friction terms. Friedrichs,Lynch, and Aubrey (1992, Chap. 15) demonstrated theimportance of frictionally dominated systems with mini-mal inertia. However, in the present system, the temporal

Fig. 8. Identification of slough network as three systems: west side,

east side, and barotropic convergence zone in the middle. Legend: ,

directions of flooding current; X, location of converging currents; .,

locations of equipment.

Fig. 9. Typical time series of velocity (a) and water level (b) at the western sites Pablo and SNS during a spring tide. The velocity exhibits a long

period of slack while the water level cannot decrease below the sill elevation. Propagation speed of flood wave is shown on the water-level plot (—,

Pablo; - - - -, SNS).


acceleration term is as important as the frictional term.The convective acceleration term is an order ofmagnitude less than the other terms, which is typicalinfrictionally dominated shallow water channels (Speer& Aubrey, 1985). At dynamic equilibrium, the accel-eration is in balance with the barotropic gradient andthe friction term.

A similar scaling for continuity leads to

qgqt

þ hqhuiqx

þ qðhuigÞqx

¼ 0 ð2Þ

10�4 10�4 10�5

temporal mean depth nonlinear

This scaling reveals that the temporal change in thewater level primarily is in balance with the spatial rateof change of the velocity times the mean depth. Thenonlinear term is an order of magnitude smaller, but itaffects the balance by altering the phase speed of thewave. Because g is in the order of the depth ðg=h� 0:3Þ, and the wave speed is a function of the depth,the wave will travel faster at high tides and slower atlow tides. This effect will produce an M4 oscillationfrom the main tidal constituent (M2).

The velocity at site Pablo during spring tides is inphase with the discharge from the slough network butthe water level is in phase with the tidal forcing fromthe bay. This creates high tide at site Pablo approxi-mately 0.5 h before the end of the flood current. Thus,the ebb will have a reduced cross-sectional area, creatinghigher ebb velocities than normally would be observed.Similar characteristics were observed by Speer, Aubrey,and Friedrichs (1991) for a tidally truncated estuary inPamet, MA. However, their truncation was caused bythe uncoupling of the interior tide from the ocean tideby very shallow depths, creating an interior balance be-tween bottom slope and friction, as opposed to a bal-ance between the barotropic pressure gradient andbottom friction as was the case with the example inSan Francisco Bay.

The velocity that develops during neap tides is moretidally symmetric due to the minimized influence of thesill (not shown). Duration of slack after ebb is dimin-ished greatly.

2.2. Barotropic convergence

Tidal signals from both sides of the system meet inthe convergence zone where it is more appropriate toconsider the role of the water-surface (barotropic) com-ponent of the pressure gradients than the propagation ofthe tide. Fig. 10a shows the water-surface elevationsduring a spring tidal period at sites Socr (west side,showing tidal truncation) and Pipe (east side). The dif-ference in the water-surface elevations (Fig. 10b) produ-ces an oscillating barotropic pressure gradient across the

middle convergence zone with a quarter-diurnal charac-teristic. The measured time series of velocity at site Hude(in the convergence zone) clearly oscillates in response tothis pressure gradient (Fig. 10c). The quarter-diurnalcharacter is greater at times of lower low water (duringspring tides). For example, at day 258.25, the water-sur-face elevation at site Socr was greater than that at sitePipe (Fig. 10a, label 1). This difference occurred becausethe west side was not able to ebb fully, owing to the sill.The east side has relatively unimpeded ebb, and, there-fore, the water level will decrease with the full tidalrange, resulting in a higher water-surface elevation onthe west side of the system driving a flow to the east.Fig. 10c shows that at this time (Fig. 10c, label 1) thereis a flow to the east at site Hude.

Because the sill delays the rising tide on the west side,the east side will receive an increasing water level firstand the response is to drive a flow to the west (Fig.10c, label 2). Until the next low tide, the oscillations inthe velocity are due to the differences in the rates of in-crease of the water levels on the west and east sides, aswell as to minor influences from the network of channels.

A momentum balance (Eq. (1)) in this convergencezone is evaluated with data from site Hude (Fig. 10d)with n¼ 0:015 and by neglecting the convective acceler-ation term. The driving force is the barotropic pressuregradient, g qg=qx, estimated as the difference in water-surface elevations between sites Pipe and Socr, dividedby an appropriate length scale of the length of HudemanSlough, approximately 4.5 km. The temporal accelera-tion term is maximum (in the order of 10�4m s2) duringtimes when the velocity at site Hude is changing direc-tion from the east to the west. This is significant to showthe dynamic nature of the wave. The size of the unsteadyterm is caused by the arrival of the wave energy, whilethe magnitude of the friction term is caused by the delayin water movement. The momentum balance shows astrong correlation between the sum of the temporaland friction terms and the barotropic pressure term. Atmoments of maximum current, a dynamic balance existsbetween the friction term and the barotropic gradient.

Momentum balance during neap tides is less dramaticbecause the tidal truncation effect is weaker. As a conse-quence, the water-surface elevations across the complexare then more nearly the same on the east and west sides(not shown) and the differences in water-surface eleva-tion do not exceed 10 cm. Resulting barotropic gradientsare not as strong as those occurring during spring tides.Hence weaker currents form at site Hude with maximumneap tidal currents in the order of 25 cm s�1. This situa-tion contrasts with the maximum spring tidal currentsthat are nearly 70 cm s�1 (Fig. 10c).

The continuity equation can be used to explain howthe quarter-diurnal velocity creates a dominant semi-diurnal water level at site Hude (not shown). Duringthe �flood� at site Hude, water approaches midslough


from both directions. Therefore, no matter which direc-tion the velocity at site Hude is heading, it will approachas an incoming flow. Thus, there must be a location atwhich the velocity is zero. The velocity gradient qu=qx(with x positive in the direction of flow) from site Hudeto the zero velocity location always will be negative.From the continuity equation: qg=qt ¼�h qu=qx, withqu=qx being negative, leads to qg=qt being positive, im-plying that the water level will be increasing in time.Consequently, even though the direction of the velocitychanges due to barotropic gradients during the flood,the water level only can increase. During the ebb, a sim-ilar process occurs with qg=qt being negative. At siteHude, independent of the direction of velocity, the waterlevel in that direction is also decreasing, which allows forthe water level at site Hude also to decrease.

2.3. Water flux

The tidally averaged flux of water through the systemis controlled by the residual barotropic gradients acrossthe convergence zone. During spring tides, the tidally

averaged water-surface elevation on the west side willbe greater than on the east side because the sill truncatesthe lower water levels on the west side, thus increasingthe mean water level and driving a tidally averaged flowto the east. Fig. 11 shows the water-surface elevation dif-ference on tidal (Fig. 11a) and tidally averaged (Fig.11b) time scales. During spring tides (day 260), the ti-dally averaged difference from the west to the east sideis negative, indicating a higher tidally averaged waterlevel on the west side. This higher water level allowsthe tidally averaged flux of water at site Hude (Fig.11c) to move towards the east. During neap tides, the ti-dally averaged water level is higher on the east side ofthe system because the propagation speed of the tide isgreater on the east side and the tidally averaged fluxof water flows to the west at site Hude (near days 254and 270).

3. Discussion

The slough network contains four convergence loca-tions (Fig. 8), including the convergence zone located

Fig. 10. Time series of water-surface elevation and velocity at the east and west sides, (a) water-surface elevations at an east site (Pipe) and west

site (Socr); (b) difference in water-surface elevation between sites Pipe and Socr; (c) velocity at site Hude, positive velocity to the west, negative to

the east; (d) momentum balance at site Hude. Legend (a): – – –, Socr (west side); ——, pipe (east side). Legend (d): ———,

ðqhui/qtÞ þ ðgn2hui j hui j /ðhþ gÞ4=3Þ; – – –, �gðdg/dxÞ:


near site Hude, identified by the direction and timing ofmeasured velocities (Warner, 2000). Location �1X� is atthe convergence of currents from two opposing sloughs.This location is characterized as a very narrow channelwith slump blocks and vegetation in the channel. Loca-tions �2X� and �4X� are characterized with shallow depthsand very narrow vegetation-choked channels. These twolocations are within one tidal excursion from San PabloBay, and have narrowed due to advection of sedimentfrom San Pablo Bay, deposition of the material, and sub-sequent lack of shear stress on the ebb that is largeenough to resuspend the material. For completeness,zone �3X� is Hudeman Slough. This slough is not subjectto the same narrowing effects because large water-surface slope gradients develop along the slough, whichproduce barotropic gradients that keep the shear stresshigh enough to prevent rapid deposition.

Convergence zones are important because they cancreate locations where sediment and dissolved substan-ces may accumulate. Also, these zones can act as trans-port pathways between two separate drainage areas.These spatial variations are consistent with observedevolutionary patterns on tidal marsh plains. For exam-ple, drainage channels can erode headwards and eventu-ally may meet with other channels, thus creating alooped channel. The end of the looped channel that re-ceives the rising tide first will dominate the residual flow

direction and then the looped channel will act to trans-port material between the drainage divides on a tidallyaveraged time scale. On a tidal time scale, the conver-gence location in the loop will tend to be characterizedwith reduced shear stress, enhancing deposition andeventually creating a drainage divide. This divide onceagain separates the channels (Collins, Collins, & Leo-pold, 1987).

4. Summary and conclusions

Circulation patterns in a channel network driven byopposing tidal entrances are characterized by the spatialand temporal asymmetries that occur in the boundingtides. Such a channel network in San Francisco Bay isaffected by a sill at the west entrance that truncatesthe water level during spring tides. The east side hasmore symmetric tidal responses. PCA was used to iden-tify the spatial influence of the truncating sill, which ledto the demarcation of the study area into three separatesystems (west side, middle, and east side). Because thewest and east sides produce different degrees of tidalasymmetry, the middle of the complex responds stronglyto the convergence of the water levels, providing a barot-ropic convergence zone.

The flux of water from the west side to the east sideoccurs through the convergence zone and is influenced

Fig. 11. Spring/neap variations of water flux past site Hude. (a) Tidal water-surface elevation difference of sites Pipe–Socr; (b) tidally averaged water-

surface elevation (WSE) differences; (c) tidally averaged water flux past site Hude to the east during spring tides and to the west during neap tides; (d)

measure of spring/neap tidal cycle.


by the spring/neap tidal cycle. Increased spring tidalranges are truncated on the west side, producing a ti-dally averaged higher water-surface elevation than onthe east side, which results in residual flows to the eastthrough Hudeman Slough. During neap tides, the tidalrange is reduced and flows are affected less by the sill.Tidally averaged flows then are to the west, due to fastertidal propagation along the Napa River as opposed tothe shallower Sonoma Creek.

Acknowledgements

The authors acknowledge support for this researchfrom the California Department of Fish and Game,the California Coastal Conservatory, the US Fish andWildlife Service Coastal Program, and the US Geologi-cal Survey Federal/State Cooperative and Place-basedPrograms.

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tidal truncation and barotropic convergence in a channel ... · the east and west asymmetric tides...

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